Nuprl Definition : ratLegendre-aux
ratLegendre-aux(n;x;tr) ==
let k,a,b = tr in
if k=n
then a
else eval k' = k + 1 in
eval a' = rat-nat-div(ratadd(int-rat-mul((2 * k) + 1;ratmul(x;a));int-rat-mul(-k;b));k') in
ratLegendre-aux(n;x;<k', a', a>)
Definitions occuring in Statement :
rat-nat-div: rat-nat-div(x;n),
int-rat-mul: int-rat-mul(n;x),
ratmul: ratmul(a;b),
ratadd: ratadd(x;y),
callbyvalue: callbyvalue,
spreadn: spread3,
int_eq: if a=b then c else d,
pair: <a, b>,
multiply: n * m,
add: n + m,
minus: -n,
natural_number: $n
Definitions occuring in definition :
spreadn: spread3,
int_eq: if a=b then c else d,
callbyvalue: callbyvalue,
rat-nat-div: rat-nat-div(x;n),
ratadd: ratadd(x;y),
add: n + m,
multiply: n * m,
natural_number: $n,
ratmul: ratmul(a;b),
int-rat-mul: int-rat-mul(n;x),
minus: -n,
pair: <a, b>
FDL editor aliases :
ratLegendre-aux
Latex:
ratLegendre-aux(n;x;tr) ==
let k,a,b = tr in
if k=n
then a
else eval k' = k + 1 in
eval a' = rat-nat-div(ratadd(int-rat-mul((2 * k) + 1;ratmul(x;a));int-rat-mul(-k;b));k') in
ratLegendre-aux(n;x;<k', a', a>)
Date html generated:
2019_10_30-AM-11_34_01
Last ObjectModification:
2019_01_10-PM-03_56_20
Theory : reals_2
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